[{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":[]},"article_processing_charge":"No","dini_type":"doc-type:article","citation":{"ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa":1,"page":"615–707","uri_base":"https://research-explorer.ista.ac.at","date_published":"2019-10-12T00:00:00Z","date_created":"2019-03-28T10:21:17Z","day":"12","publication":"Pure and Applied Analysis ","dc":{"date":["2019"],"publisher":["MSP"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"source":["Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.2140/paa.2019.1.615","info:eu-repo/semantics/altIdentifier/issn/2578-5893","info:eu-repo/semantics/altIdentifier/issn/2578-5885","info:eu-repo/semantics/altIdentifier/arxiv/1811.04055","info:eu-repo/grantAgreement/EC/FP7/338804","info:eu-repo/grantAgreement/EC/H2020/665385"],"description":["We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion."],"identifier":["https://research-explorer.ista.ac.at/record/6186"],"title":["Cusp universality for random matrices, II: The real symmetric case"],"creator":["Cipolloni, Giorgio","Erdös, László","Krüger, Torben H","Schröder, Dominik J"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"]},"type":"journal_article","article_type":"original","status":"public","_id":"6186","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"month":"10","intvolume":" 1","abstract":[{"lang":"eng"}],"oa_version":"Preprint","volume":1,"issue":"4","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"ec_funded":1,"publication_identifier":{"eissn":[],"issn":[]},"publication_status":"published","language":[{}]}]